Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circ

Fearne Castro

Fearne Castro

Answered question

2022-02-28

Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ.

Answer & Explanation

Daisie Benitez

Daisie Benitez

Beginner2022-03-01Added 5 answers

Step 1
APO=APQ=90
by circle property
Step 2
Since, OQ is perpendicular bisector of AB,
AP=BP=62=3
By Pythagoras,
OP2=OA2AP2
OP2=4232
OP=7
Similarly, QP2=QA2AP2
QP2=6232
QP=27
Hence, OQ=OP+QP
=7+27
OQ=7.842

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